Question: Multiply the following complex numbers: $({2-5i}) \cdot ({5+2i})$
Explanation: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({2-5i}) \cdot ({5+2i}) = $ $ ({2} \cdot {5}) + ({2} \cdot {2}i) + ({-5}i \cdot {5}) + ({-5}i \cdot {2}i) $ Then simplify the terms: $ (10) + (4i) + (-25i) + (-10 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ 10 + (4 - 25)i - 10i^2 $ After we plug in $i^2 = -1$ , the result becomes $ 10 + (4 - 25)i - (-10) $ The result is simplified: $ (10 + 10) + (-21i) = 20-21i $